The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows
Shifted boundary method pour systèmes hyperboliques: ondes linéaires et équations shallow water
Résumé
We propose a new computational approach for embedded boundary simulations of
hyperbolic systems. Applications are shown for the linear wave equations and for the nonlinear
shallow water system. The proposed approach belongs to the class of surrogate/approximate
boundary algorithms and is based on the idea of shifting the location where boundary conditions
are applied from the true to a surrogate boundary. Accordingly, boundary conditions, enforced
weakly, are appropriately modified to preserve optimal error convergence rates. This framework
is applied here in the setting of a stabilized finite element method, even though other spatial
discretization techniques could have been employed. Accuracy, stability and robustness of the
proposed method are tested by means of an extensive set of computational experiments for the
acoustic wave propagation equations and shallow water equations. Comparisons with standard
weak boundary conditions imposed on grids that conform to the geometry of the computational
domain boundaries are also presented.
On propose une nouvelle approche pour des simulations avec bords immergés pour des systèmes hyperboliques et en particulier les équations shallow water. L’approche proposée consiste en modifier les conditions au bords avec un développement limité permettant d’assurer l’ordre deux avec des embedded boundaries. L’approche est implementé est ici dans le cadre d’une méthode de type stabilized finite element sur un très grand nombre de cas tests représentatifs d’applications de propagation de vagues et inondation
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